Math Problem Statement
The sum of [6] consecutive even numbers is [270]. What is the second number in this sequence?
Solution
Let's solve this step-by-step.
- Let the first even number in the sequence be .
- Since we have six consecutive even numbers, the sequence will be:
- The sum of these six numbers is given as 270:
- Simplify the left side:
- Subtract 30 from both sides:
- Divide by 6:
Now, we know the first number is . The sequence is therefore:
The second number in this sequence is 42.
Would you like more details, or do you have any questions?
Here are five related questions:
- What would the first number be if the sum of six consecutive even numbers were 300?
- How do we solve for the sum of six consecutive odd numbers?
- Can we find the average of these six numbers, and how does it relate to the middle numbers?
- How would the sequence change if we had consecutive odd numbers instead?
- What would the second number be if the sequence started with 38 instead of 40?
Tip: When dealing with sequences, set up an equation to simplify the process of finding the terms.
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Math Problem Analysis
Mathematical Concepts
Algebra
Arithmetic Sequences
Formulas
Sum of arithmetic sequence
Linear equation
Theorems
Solving linear equations
Suitable Grade Level
Grades 6-8
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